Predicting continous value with CNN (prediction of fruit maturity)
but I have been told that neural networks aren't made to predict values in that way, they really are best suited for classification into discrete classes

I don't agree with this statement. I already trained many CNNs for regressions tasks where a continous output is trained and they generally perform very well.
I think the general &quot;advantage&quot; for a classification approach over a regression approach is that there is usually some margin where the output of the NN can still be clipped to a specific class, which might not be the case in regression tasks. Furthermore a lot of the &quot;better classification performance&quot; is due to the fact that the cross-entropy loss of classification tasks always tries to increase probability of one class while reducing all others. But this advantage might not be really important in your case where a specific range of days (e.g 3-5 days) can be probable instead of just one single day (e.g. exactly day 4).
Thats why I think you should defenitly try the regression approach. For this just normalize/clip your output layer to the min/max range of days. You should also defenitley decrease the learning rate at the end of training, I found this much further improves regression predictions to be more accurate.
And lastly if you want to achieve higher performance and more robustness, in your case I highly recommend a bayesian approach where you average over an ensemble of NNs (this ensemble can be your single NN with different parts truned off via Dropout layers during inferencing). With this average you can get an estimate of the uncertainty (the variance over different predictions) which gives you a much better idea of the probability distribution over the different days for a specifiy input.